How do I find the roots of a quadratic equation?

A quadratic equation is one that contains an x^2 term that has a non 0 coefficient, There are three basic methods for solving a quadratic equation; factorising, completing the square, and the quadratic formula. These methods will all work with any equation, but each one is more suited to specific sets of examples. Factorising method is based on the FACTOR THEOREM, which states that the polynomial f(x) has a factor (x-k) if f(k) =0. (this is an specific example of the more general remainder theorem). x^2-3x-28 (work through this on the whiteboard) Completing the square, this method is best suited to examples in which the roots are non-integers and thus are not easily solved by factorisation. The method involved taking half the coefficient of x and using it to create (x-k)^2 + c and then finding c by comparison. e.g. 2x^2-20x+8 The quadratic formula: this can be used to solve any quadratic equation but it is computationally intense and thus should be avoided except in the most involved cases that can not be solved by alternative methods. (state quodratic formular on the board) e.g. -7x^2+2x+9 Two final things to remember about quadratic equations are that you should always attempt to use this simplest possible method to solve the question as this will save you time. Also, you can check your answer but substituting it back into the question.